Second-Order Correction for Statistical Bias in Monte Carlo Depletion Calculations
Abstract
Depletion analyses are often driven by Monte Carlo neutron transport methods that introduce uncertainty into the transmutation matrix used to evolve a material composition. The nonlinearity of the matrix exponential applied to this transmutation matrix causes the uncertainty to introduce a systematic bias in the computed isotope vectors. This work derives a second-order correction for this bias that can be computed with quantities obtainable from typical Monte Carlo transport routines. An augmented Bateman system is formulated to evaluate these quantities and an adapted Chebyshev rational approximation method uses transmutation matrix factorizations for efficient evaluation of the second-order correction. Then, the correction is demonstrated using a ten-nuclide verification problem, an ITER port-plug activation problem, and a 9-pin boiling water reactor lattice containing self-shielded gadolinium-bearing fuel.
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BibTeX
@misc{bouvet2026secondorder,
title = {{Second-Order Correction for Statistical Bias in Monte Carlo Depletion Calculations}},
author = {Esthem Bouvet and Benoit Forget and Dean Price},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24932},
eprint = {2610.24932},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24932},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Second-Order Correction for Statistical Bias in Monte Carlo Depletion Calculations
AU - Esthem Bouvet
AU - Benoit Forget
AU - Dean Price
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.24932
UR - https://arxiv.org/abs/2610.24932
AB - Depletion analyses are often driven by Monte Carlo neutron transport methods that introduce uncertainty into the transmutation matrix used to evolve a material composition. The nonlinearity of the matrix exponential applied to this transmutation matrix causes the uncertainty to introduce a systematic bias in the computed isotope vectors. This work derives a second-order correction for this bias that can be computed with quantities obtainable from typical Monte Carlo transport routines. An augmented Bateman system is formulated to evaluate these quantities and an adapted Chebyshev rational approximation method uses transmutation matrix factorizations for efficient evaluation of the second-order correction. Then, the correction is demonstrated using a ten-nuclide verification problem, an ITER port-plug activation problem, and a 9-pin boiling water reactor lattice containing self-shielded gadolinium-bearing fuel.
ER -